Normally you should show some working or at least some idea of what you think you must do. But if [itex]P(x)=x^3+ax^2+bx+c[/itex], I can think of many cubic polynomials in which the roots will be [itex]\alpha,\beta,\alpha+\beta[/itex]. I am assuming that you are to find a cubic polynomial with leading coefficient 1 and has roots [itex]\alpha,\beta,\alpha+\beta[/itex].

Start with the relations of the roots to the coefficients.

For a cubic polynomial of the form [itex]ax^3+bx^2+cx+d=0[/itex]
[tex]\sum \alpha = \frac{-b}{a}[/tex]

[tex]\sum \alpha\beta = \frac{c}{a}[/tex]

[tex]\sum \alpha\beta\gamma =\frac{d}{a} [/tex]

(Note: [itex]\sum \alpha[/itex] denotes the sum of the roots taking one at a time)

Yes that is how to start but as I was saying before, there are many polynomials whose roots can be [itex]\alpha,\beta,\alpha+\beta[/itex]. Try solving for the roots to be in terms of the coefficients of the polynomial.